Finite Group Databasebeta

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C2×C4⋊C4×#10596833 #34020182

order18688
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×#10596833

Splittings

SylowC73 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×#64408
commutatorC2×C73C22×C4×C8
FrattiniC23C23×#64408
FittingC22×C4⋊C4×C73C4
socle, prime radicalC24×C73C22×C4
cosocleC22×Dic73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73C2×C8×C4⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C4⋊C4

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18688

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1103766);