Finite Group Databasebeta

C2×#30628256 #44536705

order31424
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#30628256

Splittings

SylowC491 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic491
commutatorC22×C491C22×C4
FrattiniC2×C4C22×D491
FittingC22×Q8×C491C2
socleC22×C491C22⋊C4
prime radicalC23×C491C2×C4
cosocleC2×C4×C491C23
hypercenterC22×Q8D491
hypocenterC491C2×#101
LCSG ▷ C22×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

4922 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 529);