Finite Group Databasebeta

C2×#27136466 #37613003

order24736
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27136466

Splittings

FittingC2×Q8×C773 ⋊ C2
SylowC773 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D773
commutator, cosocleC4×C773C23
FrattiniC4C22×D773
FittingC2×Q8×C773C2
socleC22×C773D4
prime radicalC2×D3092C2
hypercenterC2×Q8D773
hypocenterC773C2×SD16
LCSG ▷ C4×C773 ▷ C2×C773 ▷ C773
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12368

Conjugacy classes & character table

3874 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24736, 159);