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C22×C52⋊(C31⋊C3) #22604932

order9300
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C52⋊(C31⋊C3)

Splittings

Fitting, socle, HallC22×C52×C31 ⋊ C3
derived, HallC52×C31 ⋊ C22×C3
HallC22×C31 ⋊ C52⋊C3
HallC22×C52 ⋊ C31⋊C3
SylowC31 ⋊ C22×C52⋊C3
SylowC52 ⋊ C22×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC22C52⋊(C31⋊C3)
commutator, hypocenterC52×C31C22×C3
FrattiniC1G
Fitting, socleC22×C52×C31C3
LCSG ▷ C52×C31
UCSC1 ◁ C22

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×C52⋊(C31⋊C3), (C22⋊(C52⋊C3))⋊(C31⋊C3), C22×C52⋊C3×C31⋊C3, …
maximal normal subgroup ofA4×C52⋊(C31⋊C3), (C22⋊(C52⋊C3))⋊(C31⋊C3), C22×C52⋊C3×C31⋊C3, …
maximal quotient ofC22×C52⋊(C31⋊C9), C2×D3×C52⋊(C31⋊C3), C22×C3×C52⋊(C31⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 206);