Finite Group Databasebeta

C2×#30628268 #44536755

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

Aliases

direct productC2×#30628268

Splittings

SylowC491 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23C22⋊D491
commutatorC4×C491C22×C4
FrattiniC2×C4C22×D491
FittingC2×C4⋊C4×C491C2
socle, prime radicalC23×C491D4
cosocleC2×C4×C491C23
hypercenterC2×C4⋊C4D491
hypocenterC491C2×#106
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31424

Conjugacy classes & character table

4928 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 579);