Finite Group Databasebeta

C2×#13050100 #14580382

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

Aliases

direct productC2×#13050100

Splittings

SylowC41 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D164
commutatorC4×C41C22×C4
FrattiniC2×C4C22×D41
FittingC22×C8×C41C2
socleC22×C41C4⋊C4
prime radicalC23×C41Q8
cosocleC2×C4×C41C23
hypercenterC22×C8D41
hypocenterC41C2×#108
LCSG ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 595);