Finite Group Databasebeta

C2×#13050088 #14580327

order2624
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#13050088

Splittings

SylowC41 ⋊ C2×#103

Subgroups

subgroupG/H
centerC23C22⋊D41
commutatorC4×C41C22×C4
FrattiniC2×C4C22×D41
FittingC22×Q8×C41C2
socle, prime radicalC23×C41D4
cosocleC2×C4×C41C23
hypercenterC22×Q8D41
hypocenterC41C2×#103
LCSG ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2624

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 540);