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C2×C5⋊D5×C107 #24924163

order10700
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C22×C107 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C5⋊D5×C107
unambiguous semidirect product(C2×C5)⋊(D5×C107)

Splittings

Fitting, socleC2×C52×C107 ⋊ C2
derived, SylowC52 ⋊ C22×C107
HallC52×C107 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C107C5⋊D5
commutator, cosocle, hypocenterC52C22×C107
FrattiniC1G
Fitting, socleC2×C52×C107C2
LCSG ▷ C52
UCSC1 ◁ C2×C107

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2996 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C107×(C5⋊D5)⋊C3, D3×C5⋊D5×C107, C2×C3×C5⋊D5×C107, …
maximal normal subgroup ofC2×C107×(C5⋊D5)⋊C3, C2×C3×C5⋊D5×C107
maximal quotient ofD3×C5⋊D5×C107, C2×C3×C5⋊D5×C107, C2×C107×C3⋊(C5⋊D5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10700, 33);