Finite Group Databasebeta

C4×C4⋊Dic467 #44469889

order29888
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊Dic467

Splittings

SylowC467 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D467
commutatorC2×C467C2×C42
FrattiniC23C22×D467
FittingC2×C42×C467C2
socle, prime radical, cosocleC23×C467C23
hypercenterC2×C42D467
hypocenterC467C4×C4⋊C4
LCSG ▷ C2×C467 ▷ C467
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29888

Conjugacy classes & character table

7496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 401);