Finite Group Databasebeta

C22×C4⋊Dic491 #44537176

order31424
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4⋊Dic491

Splittings

SylowC491 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC24C2×D491
commutatorC2×C491C23×C4
FrattiniC22C23×D491
FittingC23×C4×C491C2
socle, prime radicalC24×C491C22
cosocleC22×C491C24
hypercenterC23×C4D491
hypocenterC491C22×C4⋊C4
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C24 ◁ C23×C4

418 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, 1000);