Finite Group Databasebeta

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#3861×Dic11⋊C5 #44568451

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct product#3861×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×#3861)
unambiguous semidirect product(C11⋊C5)⋊(C4×#3861)
unambiguous semidirect product(Dic11×#3861)⋊C5

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC72×Dic11⋊C5 ⋊ C3
HallC11⋊C5×#3861 ⋊ C4
HallDic11×#3861 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC72×Dic11 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
HallC11⋊C5 ⋊ C4×#3861
SylowC72 ⋊ C3×Dic11⋊C5
HallDic11 ⋊ C5×#3861
SylowC11 ⋊ C4×C5×#3861

Subgroups

subgroupG/H
center, Frattini, hypercenterC2AGL(1,𝔽11)×#3861
commutator, hypocenterC72×C11C3×C4×C5
Fitting, socle, cosocleC2×C72×C11C2×C3×C5
prime radicalC2×C11⋊C5×#3861C2
LCSG ▷ C72×C11
UCSC1 ◁ C2

240 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

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, 153);