Finite Group Databasebeta

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C22⋊C4×C22⋊D29 #16822311

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×C22⋊D29

Splittings

FittingC22×C22⋊C4×C29 ⋊ C2
SylowC29 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC22×C22⋊C4×C29C2
socle, cosocleC23×C29C24
prime radicalC23×C22⋊D29C2
hypercenterC22×C22⋊C4D29
hypocenterC29D4×C22⋊C4
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 928

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 7329);