Finite Group Databasebeta

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C2×C3×#11925356 #72230751

order7200
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×#11925356

Splittings

HallC32×C52 ⋊ C2×C4⋊C4
SylowC52 ⋊ C2×C3×Dic3⋊C4
SylowC32 ⋊ C2×#87832

Subgroups

subgroupG/H
center, hypercenterC22×C3#10597182
commutatorC2×C3×C52C22×C3×C4
FrattiniC2C2×C3×#10597182
Fitting, socleC22×C32×C52C2×C4
prime radicalC22×C32×C5⋊D5C22
cosocleC2×C3×C5⋊D5C23×C3
hypocenterC3×C52C2×C3×C4⋊C4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22×C3

1168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 120

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×#72224585
maximal normal subgroup ofC2×C3×#72224585

GAP

Past the SmallGroups library coverage — no SmallGroups id.