Finite Group Databasebeta

C2×C4×C4⋊Dic23 #15675732

order2944
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic23

Splittings

SylowC23 ⋊ C2×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D23
commutatorC2×C23C22×C42
FrattiniC23C23×D23
FittingC22×C42×C23C2
socle, prime radicalC24×C23C23
cosocleC23×C23C24
hypercenterC22×C42D23
hypocenterC23C2×C4×C4⋊C4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C23×C4 ◁ C22×C42

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2944

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6845);