Finite Group Databasebeta

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C22×C52×C31⋊C3 #22604934

order9300
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C52×C31⋊C3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC22×C52C31⋊C3
commutator, hypocenterC31C22×C3×C52
FrattiniC1G
Fitting, socleC22×C52×C31C3
LCSG ▷ C31
UCSC1 ◁ C22×C52

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC31⋊C3×C22⋊(C52⋊C3), C52×A4×C31⋊C3, C22×C52⋊C3×C31⋊C3, …
maximal normal subgroup ofC31⋊C3×C22⋊(C52⋊C3), C52×A4×C31⋊C3, C22×C52⋊C3×C31⋊C3, …
maximal quotient ofC22×C52×C31⋊C9, C2×C52×D3×C31⋊C3, C22×C3×C52×C31⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 208);