Finite Group Databasebeta

#117×Dic23 #15675740

order2944
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic23

Splittings

SylowC23 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D23
commutatorC2×C23C22×C42
FrattiniC23C23×D23
FittingC2×C23×#117C2
socle, cosocleC23×C23C24
prime radicalC24×C23C23
hypercenterC2×#117D23
hypocenterC23C4×#117
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6853);