Finite Group Databasebeta

C2×#13093949 #15689115

order3008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13093949

Splittings

SylowC47 ⋊ C2×#103

Subgroups

subgroupG/H
centerC23D188
commutatorC4×C47C22×C4
FrattiniC2×C4C22×D47
FittingC22×C8×C47C2
socle, prime radicalC23×C47D4
cosocleC2×C4×C47C23
hypercenterC22×C8D47
hypocenterC47C2×#103
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3008

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 541);