Finite Group Databasebeta

#108×D193 #27135303

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

Aliases

direct product#108×D193

Splittings

Fitting#108×C193 ⋊ C2
SylowC193 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D193
commutatorC4×C193C22×C4
FrattiniC2×C4C22×D193
Fitting#108×C193C2
socleC2×C193C2×C4⋊C4
prime radicalC22×D193Q8
cosocleC2×C4×C193C23
hypercenter#108D193
hypocenterC193C2×#108
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 593);