Finite Group Databasebeta

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C4⋊C4×C22⋊D227 #44402633

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4⋊C4×C22⋊D227

Splittings

FittingC22×C4⋊C4×C227 ⋊ C2
SylowC227 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D227
commutatorC22×C227C23×C4
FittingC22×C4⋊C4×C227C2
socle, cosocleC23×C227C24
prime radicalC22×C22⋊D227C22
hypercenterC22×C4⋊C4D227
hypocenterC227D4×C4⋊C4
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C23 ◁ C22×C4⋊C4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 7409);