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C2×C23×SD64 #15669879

order2944
nilpotency class5
isoclinismisoclinic class of D32
automorphism?
homologyAbelianization (H1) = C23×C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×C23×SD64

Subgroups

subgroupG/H
center, socleC22×C23D16
commutator, Frattini, cosocleC16C23×C23
prime radicalC2×C23×D16C2
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C2×C4×C23 ◁ C2×C8×C23 ◁ C2×C16×C23 ◁ G

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 57
transitive degreeμt(G) = 1472

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57);(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);(4,18)(5,33)(6,16)(7,31)(8,14)(9,29)(10,12)(11,27)(13,25)(15,23)(17,21)(20,34)(22,32)(24,30)(26,28)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C23×SD64, C23×#13652, C23×#13662, …
maximal normal subgroup ofC4×C23×SD64, C23×#13652, C23×#13662, …
maximal quotient ofC2×C23×#1415, C2×C23×#1416, C2×C23×#1424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 992);