C₃×C₂₃×D₂₉ #16860692

order	4002
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₂₃×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂×C₃×C₂₃)

Splittings

Fitting, socle, Hall	C₃×C₂₃×C₂₉ ⋊ C₂
derived, Sylow	C₂₉ ⋊ C₂×C₃×C₂₃
Hall	C₂₃×C₂₉ ⋊ C₂×C₃
Hall	C₃×C₂₉ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₂₃×C₂₉	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₃×C₂₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 2001

A minimal faithful permutation representation — 2 generators on 55 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);(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

1104 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₃×D₂₉, C₃×C₂₃×D₈₇, C₃²×C₂₃×D₂₉, …
maximal normal subgroup of	C₉×C₂₃×D₂₉, C₃²×C₂₃×D₂₉, C₃×C₅×C₂₃×D₂₉, …
maximal quotient of	C₉×C₂₃×D₂₉, C₃×C₂₃×D₈₇, C₃²×C₂₃×D₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4002, 2);

C3×C23×D29 #16860692