Finite Group Databasebeta

#97×D172 #25095058

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct product#97×D172

Splittings

FittingC4×#97×C43 ⋊ C2
SylowC43 ⋊ D4×#97

Subgroups

subgroupG/H
center, FrattiniC22×C4C23×D43
commutatorC22×C43C22×C42
FittingC4×#97×C43C2
socleC23×C43C23×C4
prime radicalC22×D172C2×C4
cosocleC22×C4×C43C24
hypercenterC4×#97D43
hypocenterC43D4×#97
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#97

1274 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 168029);