Finite Group Databasebeta

C4×#10624999 #15673286

order2944
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#10624999

Splittings

SylowC23 ⋊ C4×#106

Subgroups

subgroupG/H
centerC22×C4D92
commutatorC4×C23C2×C42
FrattiniC22×C4C22×D23
FittingC2×C4×C8×C23C2
socle, prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenterC2×C4×C8D23
hypocenterC23C4×#106
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

280 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

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, 4399);