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C22×D32×D4 #11919164

order1152
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C215

Aliases

direct productC22×D32×D4

Splittings

FittingC22×C32×D4 ⋊ C22
SylowC32 ⋊ C24×D4

Subgroups

subgroupG/H
centerC23C22×D32
commutator, cosocleC2×C32C26
FrattiniC2C24×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C24×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

21785 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 96

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#11902326, C2×#11902357, #72219800, …
maximal normal subgroup ofC2×#11902326, C2×#11902357, #72219800, …
maximal quotient of#72213893, #72215068, C2×#11902326, …
automorphism group of#63568, #63569, #63570, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 153175);