Finite Group Databasebeta

← Prev (#10587222) Next (#10587224) →

C11⋊(#41⋊C3) #10587223

order528
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC11⋊(#41⋊C3)
unambiguous semidirect product#4343⋊C3

Splittings

Hall#4343 ⋊ C3
SylowC11 ⋊ #41⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2A4×D11
commutator, Fitting, cosocle, hypocenterQ8×C11C2×C3
socleC2×C11C2×A4
LCSG ▷ Q8×C11
UCSC1 ◁ C2

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 176

Polycyclic presentation:

2,3,2^2,11,2|a^2=f,c^2=f,d^2=f,e^a=e^10,c^b=cd,d^b=c,d^c=df

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11761317, #11761318, #11761319, …
maximal normal subgroup of#11761317, #11761318, #11761319, …
maximal quotient ofSL(2,𝔽3)×Dic11, C2×C11⋊(#41⋊C3), C11⋊(#41⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 93);