Finite Group Databasebeta

#27135105

order12352
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C42

Aliases

No aliases for this group.

Splittings

SylowC193 ⋊ #376

Subgroups

subgroupG/H
centerC22×C4C2×D193
commutatorC2×C193C2×C42
FrattiniC23C22×D193
FittingC2×C42×C193C2
socle, prime radical, cosocleC23×C193C23
hypercenterC2×C42D193
hypocenterC193#376
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22×C4 ◁ C2×C42

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,193|a^2=e,b^2=f,c^2=d,b^a=bd,g^b=g^192

Conjugacy classes & character table

3112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 395);