C₂×D₅₉₂₅ #37557157

order	23700
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₁₈₅₀
direct product	C₂×D₅₉₂₅
unambiguous semidirect product	(C₂×C₃)⋊D₁₉₇₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₂₃₇
unambiguous semidirect product	(C₂×C₇₉)⋊D₇₅

Splittings

Fitting	C₂×C₃×C₂₅×C₇₉ ⋊ C₂
derived, Hall	C₃×C₂₅×C₇₉ ⋊ C₂²
Hall	C₂₅×C₇₉ ⋊ C₂×D₃
Hall	C₃×C₇₉ ⋊ C₂×D₂₅
Sylow	C₇₉ ⋊ C₂×D₇₅
Hall	C₃×C₂₅ ⋊ C₂×D₇₉
Sylow	C₂₅ ⋊ C₂×D₂₃₇
Sylow	C₃ ⋊ C₂×D₁₉₇₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₅₉₂₅
commutator, cosocle, hypocenter	C₃×C₂₅×C₇₉	C₂²
Frattini	C₅	C₂×D₁₁₈₅
Fitting	C₂×C₃×C₂₅×C₇₉	C₂
socle	C₂×C₃×C₅×C₇₉	D₅
LCS	G ▷ C₃×C₂₅×C₇₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 109
transitive degree	μ_t(G) = 11850

A minimal faithful permutation representation — 2 generators on 109 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);(4,5)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(32,109)(33,108)(34,107)(35,106)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Conjugacy classes & character table

5928 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₃₇₀₀
maximal normal subgroup of	D₂₃₇₀₀
maximal quotient of	Dic₁₁₈₅₀, D₂₃₇₀₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23700, 40);

C2×D5925 #37557157