Finite Group Databasebeta

#27135312

order12352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC193 ⋊ #431

Subgroups

subgroupG/H
centerC42C2×D193
commutatorC2×C193C22×C8
FrattiniC2×C4C22×D193
FittingC2×C42×C193C2
socleC22×C193C22×C4
prime radicalC23×C193C2×C4
cosocleC2×C4×C193C23
hypercenterC2×C42D193
hypocenterC193#431
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C42 ◁ C2×C42

118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^6,193|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=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, 602);