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C2×C32×D32 #11769308

order1152
nilpotency class5
isoclinismisoclinic class of D32
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C32×D32

Subgroups

subgroupG/H
center, socleC22×C32D16
commutator, Frattini, cosocleC16C23×C32
LCSG ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C32 ◁ C2×C32×C4 ◁ C2×C32×C8 ◁ C2×C32×C16 ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 40
transitive degreeμt(G) = 576

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2)(35,36,37);(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)(38,39,40);(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)

Conjugacy classes & character table

342 conjugacy classes — view the full character table.

Relationships

Fitting subgroup ofC2×C3⋊D3×D32, #72269638
maximal subgroup ofC32×#13654, C2×C3⋊D3×D32, #72269638
maximal normal subgroup ofC32×#13654, C2×C3⋊D3×D32, #72269638

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 3319);