Finite Group Databasebeta

#101×D193 #27135237

order12352
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×D193

Splittings

Fitting#101×C193 ⋊ C2
SylowC193 ⋊ C2×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×D193
commutatorC22×C193C22×C4
FrattiniC2×C4C22×D193
Fitting#101×C193C2
socleC2×C193C2×C22⋊C4
prime radicalC22×D193C2×C4
cosocleC2×C4×C193C23
hypercenter#101D193
hypocenterC193C2×#101
LCSG ▷ C22×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1078 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 527);