D₁₃×C₉₇ #14578992

order	2522
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₃×C₉₇
unambiguous semidirect product	C₁₃⋊(C₂×C₉₇)

Splittings

Fitting, socle, Hall	C₁₃×C₉₇ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₉₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₉₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₉₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₉₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 110
transitive degree	μ_t(G) = 1261

A minimal faithful permutation representation — 2 generators on 110 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×D₁₃×C₉₇, C₉₇×D₆₅, C₇×D₁₃×C₉₇, …
maximal normal subgroup of	C₅×D₁₃×C₉₇, C₇×D₁₃×C₉₇, C₁₁×D₁₃×C₉₇, …
maximal quotient of	C₅×D₁₃×C₉₇, C₉₇×D₆₅, C₇×D₁₃×C₉₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2522, 1);

D13×C97 #14578992