Finite Group Databasebeta

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#117×#595 #14545217

order2176
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×#595

Splittings

FittingC17×#117 ⋊ C4
SylowC17 ⋊ C4×#117

Subgroups

subgroupG/H
centerC2×C4C22×#595
commutatorC2×C17C22×C42
FrattiniC22C23×#595
FittingC17×#117C4
socleC22×C17C23×C4
prime radicalC23×D17C23
cosocleC22×D17C24
hypercenter#117#595
hypocenterC17C4×#117
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #117

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 272

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofH(3,ℤ/4)×#595, #339×#595, #17956610, …
maximal normal subgroup ofH(3,ℤ/4)×#595, #339×#595, #17956610, …
maximal quotient of#376×#595, C4×C22⋊C4×#595, C4×C4⋊C4×#595, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2176, 20943);