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C2×D3×#525 #11701838

order768
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC2×D3×#525

Splittings

FittingC2×C3×#525 ⋊ C2
SylowC3 ⋊ C22×#525

Subgroups

subgroupG/H
centerC22×C4C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#525C2
socleC23×C3C25
hypercenterC2×#525D3
hypocenterC3C22×#525
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#525

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D3×#3484, C2×D3×#3003, C22×D3×#525, …
maximal normal subgroup ofC2×D3×#3484, C2×D3×#3003, C22×D3×#525, …
maximal quotient ofC2×C4×D3×#120, C2×D3×#2847, C22×D3×#525, …
automorphism group ofC4⋊(C3⋊C16), Dic3×C16, #4502, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1076219);