Finite Group Databasebeta

C2×#30628272 #44536770

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

Aliases

direct productC2×#30628272

Splittings

SylowC491 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4C22⋊D491
commutatorC4×C491C22×C4
FrattiniC2×C4C22×D491
FittingC2×M16×C491C2
socleC22×C491C4⋊C4
prime radicalC23×C491Q8
cosocleC2×C4×C491C23
hypercenterC2×M16D491
hypocenterC491C2×#108
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

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, 594);