Finite Group Databasebeta

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C2×C4⋊C4×Dic227 #44402071

order29056
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4⋊C4×Dic227

Splittings

SylowC227 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×D227
commutatorC2×C227C22×C42
FrattiniC23C23×D227
FittingC22×C4⋊C4×C227C2
socle, prime radicalC24×C227C23
cosocleC23×C227C24
hypercenterC22×C4⋊C4D227
hypocenterC227C2×C4×C4⋊C4
LCSG ▷ C2×C227 ▷ C227
UCSC1 ◁ C24 ◁ C22×C4⋊C4

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29056

Conjugacy classes & character table

4600 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 6847);