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C4×C103⋊C17 #20296207

order7004
automorphism?
homologyAbelianization (H1) = C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC4×C103⋊C17
unambiguous semidirect product(C4×C103)⋊C17

Splittings

Fitting, HallC4×C103 ⋊ C17
derived, SylowC103 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC4C103⋊C17
commutator, hypocenterC103C4×C17
FrattiniC2C2×C103⋊C17
FittingC4×C103C17
socleC2×C103C2×C17
LCSG ▷ C103
UCSC1 ◁ C4

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C4×C103⋊C17, C4×(C103⋊C3)⋊C17, Dic3×C103⋊C17, …
maximal normal subgroup ofC3×C4×C103⋊C17, C4×(C103⋊C3)⋊C17, C4×C5×C103⋊C17
maximal quotient ofC3×C4×C103⋊C17, Dic3×C103⋊C17, C4×C5×C103⋊C17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7004, 3);