Finite Group Databasebeta

#97×D367 #37554133

order23488
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct product#97×D367

Splittings

Fitting#97×C367 ⋊ C2
SylowC367 ⋊ C2×#97

Subgroups

subgroupG/H
center, FrattiniC2×C4C22×D367
commutatorC2×C367C2×C42
Fitting#97×C367C2
socleC22×C367C22×C4
prime radicalC22×D367C2×C4
cosocleC2×C4×C367C23
hypercenter#97D367
hypocenterC367C2×#97
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C2×C4 ◁ #97

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

3700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 496);