Finite Group Databasebeta

← Prev (#10596670) Next (#10596672) →

C2×D32×D4 #10596671

order576
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×D32×D4

Splittings

FittingC2×C32×D4 ⋊ C22
SylowC32 ⋊ C23×D4

Subgroups

subgroupG/H
centerC22C22×D32
commutator, cosocleC2×C32C25
FrattiniC2C23×D32
FittingC2×C32×D4C22
socleC22×C32C24
hypercenterC2×D4D32
hypocenterC32C23×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

2842 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 48

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11784609, #11784648, #11784717, …
maximal normal subgroup of#11784609, #11784648, #11784717, …
maximal quotient ofC2×D32×C22⋊C4, C2×D32×C4⋊C4, C4×D32×D4, …
automorphism group of#3714, #3715, #3716, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8553);