Finite Group Databasebeta

C2×#30628273 #44536771

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

Aliases

direct productC2×#30628273

Splittings

SylowC491 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1964
commutatorC4×C491C22×C4
FrattiniC2×C4C22×D491
FittingC22×C8×C491C2
socleC22×C491C4⋊C4
prime radicalC23×C491Q8
cosocleC2×C4×C491C23
hypercenterC22×C8D491
hypocenterC491C2×#108
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

7868 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 595);