Finite Group Databasebeta

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#97×#92314 #72254641

order15552
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C23×C3

Aliases

direct product#97×#92314

Splittings

Fitting#97×#6900 ⋊ C2
Sylow#6900 ⋊ C2×#97

Subgroups

subgroupG/H
centerC2×C4C22×#92314
commutatorC2×C92C2×C3×C42
FrattiniC2×C32×C4C22×C3×C3⋊D3
Fitting#97×#6900C2
socleC22×C32C2×C3×C4×C3⋊D3
prime radicalC22×#92314C2×C4
cosocleC2×C4×C92C23×C3
hypercenter#97#92314
hypocenterC92C2×C3×#97
LCSG ▷ C2×C92 ▷ C92
UCSC1 ◁ C2×C4 ◁ #97

3598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2592

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.