Finite Group Databasebeta

#123×Dic23 #15675920

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#123×Dic23

Splittings

SylowC23 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC2×C23×#123C2
socle, cosocleC23×C23C24
prime radicalC22×D4×C23C22
hypercenterC2×#123D23
hypocenterC23C4×#123
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×#123

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7033);