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C2×C52×C7×D17 #26045469

order11900
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C22×C52×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×C7×D17
unambiguous semidirect productC17⋊(C22×C52×C7)
unambiguous semidirect product(C2×C17)⋊(C2×C52×C7)

Splittings

Fitting, socleC2×C52×C7×C17 ⋊ C2
derived, SylowC17 ⋊ C22×C52×C7
HallC52×C7×C17 ⋊ C22
HallC52×C17 ⋊ C22×C7
HallC7×C17 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52×C7D17
commutator, cosocle, hypocenterC17C22×C52×C7
FrattiniC1G
Fitting, socleC2×C52×C7×C17C2
LCSG ▷ C17
UCSC1 ◁ C2×C52×C7

160 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×D17×C52⋊C3, C2×D17×C7⋊(C52⋊C3), C2×C52×ΓL(1,𝔽8)×D17, …
maximal normal subgroup ofC2×C7×D17×C52⋊C3, C2×D17×C7⋊(C52⋊C3), C2×C52×ΓL(1,𝔽8)×D17, …
maximal quotient ofC52×D3×C7×D17, C2×C3×C52×C7×D17, C2×C52×C7×D51

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 118);