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C2×C112×C5⋊D5 #27131000

order12100
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C112 · Schur multiplier (H2) = C2×C5×C11

Aliases

direct productC2×C112×C5⋊D5
unambiguous semidirect product(C2×C5)⋊(D5×C112)

Splittings

Fitting, socleC2×C52×C112 ⋊ C2
derived, SylowC52 ⋊ C22×C112
HallC52×C112 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C112C5⋊D5
commutator, cosocle, hypocenterC52C22×C112
FrattiniC1G
Fitting, socleC2×C52×C112C2
LCSG ▷ C52
UCSC1 ◁ C2×C112

560 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3388 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×(C5⋊D5)⋊(C112⋊C3), C2×C112×(C5⋊D5)⋊C3, C2×C5⋊D5×C112⋊C3, …
maximal normal subgroup ofC2×(C5⋊D5)⋊(C112⋊C3), C2×C112×(C5⋊D5)⋊C3, C2×C5⋊D5×C112⋊C3, …
maximal quotient ofD3×C112×C5⋊D5, C2×C3×C112×C5⋊D5, C2×C112×C3⋊(C5⋊D5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12100, 279);