Finite Group Databasebeta

← Prev (#23756147) Next (#23756149) →

C17×#10596872 #23756148

order9996
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×#10596872

Splittings

derived, SylowC72 ⋊ C3×C4×C17
HallC7×C17×Dic7 ⋊ C3
HallC17×#3862 ⋊ C4
HallC72×C17 ⋊ C3×C4
HallC7×Dic7 ⋊ C3×C17
Hall#3862 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17#64422
commutator, hypocenterC72C3×C4×C17
FrattiniC2C17×#64422
Fitting, socleC2×C72×C17C2×C3
prime radicalC2×C17×#3862C2
cosocleC2×C72C2×C3×C17
LCSG ▷ C72
UCSC1 ◁ C2×C17

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC17×ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4, C3×C17×#10596872, C17×C3⋊#10596872
maximal normal subgroup ofC17×ΓL(1,𝔽8)×ΓL(1,𝔽8)⋊C4, C3×C17×#10596872
maximal quotient ofC17×#13183531, C3×C17×#10596872, C17×C3⋊#10596872

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9996, 51);