C₁₁×Dic₉₅ #16862015

order	4180
isoclinism	isoclinic class of D₉₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×Dic₉₅
unambiguous semidirect product	C₁₉⋊(C₁₁×Dic₅)

Splittings

derived, Hall	C₅×C₁₉ ⋊ C₄×C₁₁
Hall	C₅×C₁₁×C₁₉ ⋊ C₄
Hall	C₁₁×C₁₉ ⋊ Dic₅
Hall	C₅×C₁₁ ⋊ Dic₁₉
Sylow	C₁₉ ⋊ C₁₁×Dic₅
Sylow	C₅ ⋊ C₁₁×Dic₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₉₅
commutator, hypocenter	C₅×C₁₉	C₄×C₁₁
Frattini	C₂	C₁₁×D₉₅
Fitting, socle, prime radical	C₂×C₅×C₁₁×C₁₉	C₂
cosocle	C₂×C₅×C₁₉	C₂×C₁₁
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₁₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 4180

A minimal faithful permutation representation — 2 generators on 39 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);(12,14,13,15)(17,20)(18,19)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×Dic₉₅, C₁₁×Dic₂₈₅, C₁₁×(C₁₉⋊C₃)⋊Dic₅, …
maximal normal subgroup of	C₃×C₁₁×Dic₉₅, C₁₁×(C₁₉⋊C₃)⋊Dic₅, C₁₁⋊C₅×Dic₉₅, …
maximal quotient of	C₃×C₁₁×Dic₉₅, C₁₁×Dic₂₈₅, C₁₁×Dic₄₇₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4180, 7);

C11×Dic95 #16862015