Finite Group Databasebeta

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#3862×Dic11⋊C5 #44568452

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C7

Aliases

direct product#3862×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×#3862)
unambiguous semidirect product(C11⋊C5)⋊(C4×#3862)
unambiguous semidirect product(Dic11×#3862)⋊C5

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC72×Dic11⋊C5 ⋊ C3
HallC11⋊C5×#3862 ⋊ C4
HallDic11×#3862 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC72×Dic11 ⋊ C3×C5
HallC11×#3862 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×#3862
SylowC72 ⋊ C3×Dic11⋊C5
HallDic11 ⋊ C5×#3862
SylowC11 ⋊ C4×C5×#3862

Subgroups

subgroupG/H
center, Frattini, hypercenterC2AGL(1,𝔽11)×#3862
commutator, hypocenterC72×C11C3×C4×C5
Fitting, socle, cosocleC2×C72×C11C2×C3×C5
prime radicalC2×C11⋊C5×#3862C2
LCSG ▷ C72×C11
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 924

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 154);