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Cayley diagram

C2×#6296 #89048

order432
isoclinismisoclinic class of #6295
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#6296

Splittings

SylowC33 ⋊ C2×Q8

Subgroups

subgroupG/H
center, hypercenterC22#1113
commutator, cosocleC2×C33C23
FrattiniC2C2×#1113
Fitting, socle, prime radicalC22×C33C22
hypocenterC33C2×Q8
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22

210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 48

A minimal faithful permutation representation — 3 generators on 19 points:

(4,5)(6,7,8)(9,10)(12,14,15,19)(13,16,17,18);(3,4,5)(7,8)(10,11)(12,13,15,17)(14,18,19,16);(1,2)

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11722774, #11722794, #11722944, …
maximal normal subgroup of#11722774, #11722794, #11722944, …
maximal quotient of#11723680, C4×#6296, C4⋊#6296, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 695);