Finite Group Databasebeta

C4×C4⋊Dic491 #44536577

order31424
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×C4⋊Dic491

Splittings

SylowC491 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C2×D491
commutatorC2×C491C2×C42
FrattiniC23C22×D491
FittingC2×C42×C491C2
socle, prime radical, cosocleC23×C491C23
hypercenterC2×C42D491
hypocenterC491C4×C4⋊C4
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C22×C4 ◁ C2×C42

194 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31424

Conjugacy classes & character table

7880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 401);