Finite Group Databasebeta

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C2×C52×D93 #22604939

order9300
isoclinismisoclinic class of D93
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×D93
unambiguous semidirect product(C2×C3)⋊(C52×D31)

Splittings

Fitting, socleC2×C3×C52×C31 ⋊ C2
derived, HallC3×C31 ⋊ C22×C52
HallC3×C52×C31 ⋊ C22
HallC52×C31 ⋊ C2×D3
HallC3×C52 ⋊ C2×D31
SylowC31 ⋊ C2×C52×D3
SylowC3 ⋊ C2×C52×D31

Subgroups

subgroupG/H
center, hypercenterC2×C52D93
commutator, hypocenterC3×C31C22×C52
FrattiniC1G
Fitting, socleC2×C3×C52×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C2×C52

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C52×D279, C2×C3⋊(D31⋊(C52⋊C3)), C2×C52⋊C3×D93, …
maximal normal subgroup ofC2×C3⋊(D31⋊(C52⋊C3)), C2×C52⋊C3×D93, C2×C52×C3⋊(D31⋊C3), …
maximal quotient ofC2×C52×D279, C52×D3×D93, C2×C3×C52×D93, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 213);