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C7×#13133353 #26045441

order11900
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC7×#13133353

Splittings

Fitting, socle, HallC52×C7×C17 ⋊ C4
derived, HallC52×C17 ⋊ C4×C7
HallC52×C7 ⋊ #595
HallC7×C17 ⋊ #1039
SylowC52 ⋊ C7×#595
SylowC17 ⋊ C7×#1039

Subgroups

subgroupG/H
center, hypercenterC7#13133353
commutator, hypocenterC52×C17C4×C7
FrattiniC1G
Fitting, socleC52×C7×C17C4
prime radicalC52×C7×D17C2
cosocleC52×D17C2×C7
LCSG ▷ C52×C17
UCSC1 ◁ C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

896 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×#13133353⋊C3, #13133353⋊ΓL(1,𝔽8), ΓL(1,𝔽8)×#13133353, …
maximal normal subgroup ofC7×#13133353⋊C3, #13133353⋊ΓL(1,𝔽8), ΓL(1,𝔽8)×#13133353, …
maximal quotient ofC3×C7×#13133353, C7×C3⋊#13133353

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 90);