C₂×C₂₉⋊((C₅⋊D₅)⋊C₉) #39907916

order	26100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₂₉⋊((C₅⋊D₅)⋊C₉)
unambiguous semidirect product	(C₂×C₂₉)⋊((C₅⋊D₅)⋊C₉)
unambiguous semidirect product	(C₂×C₅⋊D₁₄₅)⋊C₉

Splittings

derived, Hall	C₅²×C₂₉ ⋊ C₂²×C₉
Hall	C₂₉×C₅²⋊C₉ ⋊ C₂²
Hall	C₂×C₅⋊D₁₄₅ ⋊ C₉
Hall	C₅²⋊C₉ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ C₂×(C₅⋊D₅)⋊C₉
Sylow	C₅² ⋊ C₂×C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂₉⋊((C₅⋊D₅)⋊C₃)
commutator, hypocenter	C₅²×C₂₉	C₂²×C₉
Frattini	C₃	C₂×C₂₉⋊((C₅⋊D₅)⋊C₃)
Fitting, socle	C₂×C₃×C₅²×C₂₉	C₂×C₃
prime radical	C₂×C₃×C₅⋊D₁₄₅	C₃
cosocle	C₃×C₅²×C₂₉	C₂²×C₃
LCS	G ▷ C₅²×C₂₉
UCS	C₁ ◁ C₂×C₃

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 2610

A minimal faithful permutation representation — 2 generators on 55 points:

(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)(30,31,33)(32,42,38,35,36,44)(34,39,43,40,41,37)(45,49,53,47,52,48,50,46,51);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(30,32,37,43,35)(31,34,36,42,40)(33,38,39,41,44)(54,55)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 150);

C2×C29⋊((C5⋊D5)⋊C9) #39907916