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3−1+2×C43⋊C9 #23782791

order10449
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C32

Aliases

direct product3−1+2×C43⋊C9

Splittings

SylowC43 ⋊ C9×3−1+2

Subgroups

subgroupG/H
center, FrattiniC32C32×C43⋊C3
commutatorC3×C43C32×C9
FittingC3×3−1+2×C43C3
socle, cosocleC32×C43C33
prime radicalC33×C43C32
hypercenterC3×3−1+2C43⋊C3
hypocenterC43C9×3−1+2
LCSG ▷ C3×C43 ▷ C43
UCSC1 ◁ C32 ◁ C3×3−1+2

148 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#44532440, #44532442, #44532444, …
maximal normal subgroup of#44532440, #44532442, #44532444, …
maximal quotient ofC32⋊C9×C43⋊C9, C9⋊C9×C43⋊C9, #44532280, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10449, 175);