Finite Group Databasebeta

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#453×#3633 #72242844

order8704
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct product#453×#3633

Splittings

FittingC17×#453 ⋊ C8
SylowC17 ⋊ C8×#453

Subgroups

subgroupG/H
centerC2#120×#3633
commutatorC2×C4×C17C23×C8
FrattiniC2×C4C23×#3633
FittingC17×#453C8
socleC2×C17C8×#120
prime radicalD17×#453C4
cosocleC2×C4×#595C24
hypercenter#453#3633
hypocenterC17C8×#453
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

2316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 136

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#453×AGL(1,𝔽17), #3633×#5935
maximal normal subgroup of#453×AGL(1,𝔽17)

GAP

Past the SmallGroups library coverage — no SmallGroups id.