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C7×(C103⋊C3)⋊C4 #22575740

order8652
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C103⋊C3)⋊C4
unambiguous semidirect product(C103⋊C3)⋊(C4×C7)
unambiguous semidirect productDic103⋊(C3×C7)

Splittings

derived, SylowC103 ⋊ C3×C4×C7
HallC7×Dic103 ⋊ C3
HallC7×C103⋊C3 ⋊ C4
HallC7×C103 ⋊ C3×C4
HallDic103 ⋊ C3×C7
HallC103⋊C3 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D103⋊C3
commutator, hypocenterC103C3×C4×C7
FrattiniC2C7×D103⋊C3
Fitting, socleC2×C7×C103C2×C3
LCSG ▷ C103
UCSC1 ◁ C2×C7

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

322 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×(C103⋊C3)⋊C4, C3×C7×(C103⋊C3)⋊C4, C7×C3⋊((C103⋊C3)⋊C4)
maximal normal subgroup ofΓL(1,𝔽8)×(C103⋊C3)⋊C4, C3×C7×(C103⋊C3)⋊C4
maximal quotient ofC7×Dic103⋊C9, C3×C7×(C103⋊C3)⋊C4, C7×C3⋊((C103⋊C3)⋊C4)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8652, 13);