Finite Group Databasebeta

C4×#10625001 #15673299

order2944
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#10625001

Splittings

SylowC23 ⋊ C4×#108

Subgroups

subgroupG/H
centerC42D92
commutatorC4×C23C2×C42
FrattiniC22×C4C22×D23
FittingC2×C4×C8×C23C2
socleC22×C23C2×C4⋊C4
prime radicalC23×C23C2×Q8
cosocleC22×C4×C23C23
hypercenterC2×C4×C8D23
hypocenterC23C4×#108
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 4412);