Finite Group Databasebeta

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C11×#15668773 #44568643

order32340
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#15668773

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ Dic3
derived, HallC5×#3862 ⋊ C4×C11
HallC5×C11×#3862 ⋊ C4
HallC11×#3862 ⋊ AGL(1,𝔽5)
HallC72×C11 ⋊ ΓL(1,𝔽16)
HallC5×C72 ⋊ C11×Dic3
Hall#3862 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ #10596868
SylowC72 ⋊ C11×ΓL(1,𝔽16)
SylowC5 ⋊ C11×#10596868

Subgroups

subgroupG/H
center, hypercenterC11#15668773
commutator, hypocenterC5×#3862C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11Dic3
prime radicalD5×C11×#3862C2
cosocleD5×#3862C2×C11
LCSG ▷ C5×#3862
UCSC1 ◁ C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

649 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 345);