Finite Group Databasebeta

C4⋊C4×Dic58 #16822407

order3712
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic58

Splittings

SylowC29 ⋊ Q8×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D29
commutatorC22×C29C23×C4
FittingC4×C4⋊C4×C29C2
socle, prime radical, cosocleC23×C29C24
hypercenterC4×C4⋊C4D29
hypocenterC29Q8×C4⋊C4
LCSG ▷ C22×C29 ▷ C29
UCSC1 ◁ C23 ◁ C4×C4⋊C4

568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3712

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, 7425);