Finite Group Databasebeta

C2×#28415437 #44446387

order29728
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28415437

Splittings

FittingC2×Q8×C929 ⋊ C2
SylowC929 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D929
commutator, cosocleC4×C929C23
FrattiniC4C22×D929
FittingC2×Q8×C929C2
socleC22×C929D4
prime radicalC2×D3716C2
hypercenterC2×Q8D929
hypocenterC929C2×SD16
LCSG ▷ C4×C929 ▷ C2×C929 ▷ C929
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14864

Conjugacy classes & character table

4654 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29728, 159);