Finite Group Databasebeta

C2×#23752229 #34077652

order19328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#23752229

Splittings

SylowC151 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting, prime radicalC22×#41×C151C2
socleC22×C151C2×C22⋊C4
cosocleC2×C4×C151C24
hypercenterC22×#41D151
hypocenterC151C2×#421
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#41

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4832

Conjugacy classes & character table

3044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 13052);