Finite Group Databasebeta

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C2×C4⋊C4×Dic178 #36713730

order22784
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4⋊C4×Dic178

Splittings

SylowC89 ⋊ C2×Q8×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D89
commutatorC22×C89C24×C4
FrattiniC23C24×D89
FittingC2×C4×C4⋊C4×C89C2
socle, prime radicalC24×C89C24
cosocleC23×C89C25
hypercenterC2×C4×C4⋊C4D89
hypocenterC89C2×Q8×C4⋊C4
LCSG ▷ C22×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

3246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22784

Conjugacy classes & character table

3620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22784, 328870);