Finite Group Databasebeta

#121×Dic151 #34071624

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

Aliases

direct product#121×Dic151

Splittings

SylowC151 ⋊ C4×#121

Subgroups

subgroupG/H
center, FrattiniC23C23×D151
commutatorC22×C151C23×C4
Fitting, prime radicalC2×#121×C151C2
socle, cosocleC23×C151C24
hypercenterC2×#121D151
hypocenterC151C4×#121
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#121

824 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 7024);