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C7×#13133334 #26045396

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

Aliases

direct productC7×#13133334

Splittings

derived, HallC52×C17 ⋊ C4×C7
HallC52×C7×C17 ⋊ C4
HallC52×C7 ⋊ Dic17
HallC7×C17 ⋊ #1039
SylowC52 ⋊ C7×Dic17
SylowC17 ⋊ C7×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊D85
commutator, hypocenterC52×C17C4×C7
FrattiniC2C7×C5⋊D85
Fitting, socle, prime radicalC2×C52×C7×C17C2
cosocleC2×C52×C17C2×C7
LCSG ▷ C52×C17
UCSC1 ◁ C2×C7

96 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 ofΓL(1,𝔽8)×#13133334, C7×#13133334⋊C3, #13133334⋊ΓL(1,𝔽8), …
maximal normal subgroup ofΓL(1,𝔽8)×#13133334, C7×#13133334⋊C3, #13133334⋊ΓL(1,𝔽8), …
maximal quotient ofC7×C3⋊#13133334, C3×C7×#13133334

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11900, 45);