C₁₃×D₁₂₇ #15693238

order	3302
isoclinism	isoclinic class of D₁₂₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₁₂₇
unambiguous semidirect product	C₁₂₇⋊(C₂×C₁₃)

Splittings

Fitting, socle, Hall	C₁₃×C₁₂₇ ⋊ C₂
derived, Sylow	C₁₂₇ ⋊ C₂×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₁₂₇
commutator, cosocle, hypocenter	C₁₂₇	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₂₇	C₂
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₁₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 140
transitive degree	μ_t(G) = 1651

A minimal faithful permutation representation — 2 generators on 140 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140);(15,140)(16,139)(17,138)(18,137)(19,136)(20,135)(21,134)(22,133)(23,132)(24,131)(25,130)(26,129)(27,128)(28,127)(29,126)(30,125)(31,124)(32,123)(33,122)(34,121)(35,120)(36,119)(37,118)(38,117)(39,116)(40,115)(41,114)(42,113)(43,112)(44,111)(45,110)(46,109)(47,108)(48,107)(49,106)(50,105)(51,104)(52,103)(53,102)(54,101)(55,100)(56,99)(57,98)(58,97)(59,96)(60,95)(61,94)(62,93)(63,92)(64,91)(65,90)(66,89)(67,88)(68,87)(69,86)(70,85)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)

Conjugacy classes & character table

845 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₁₃×D₁₂₇, C₁₃×D₆₃₅, C₇×C₁₃×D₁₂₇, …
maximal normal subgroup of	C₅×C₁₃×D₁₂₇, C₇×C₁₃×D₁₂₇, C₁₃×D₁₂₇⋊C₇, …
maximal quotient of	C₅×C₁₃×D₁₂₇, C₁₃×D₆₃₅, C₇×C₁₃×D₁₂₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3302, 2);

C13×D127 #15693238