Finite Group Databasebeta

← Prev (#31798207) Next (#31798209) →

C11×#13097582 #31798208

order17556
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#13097582

Splittings

derived, HallC7×C19 ⋊ C3×C4×C11
HallC7×C11×Dic19 ⋊ C3
HallC11×#87704 ⋊ C4
HallC7×C11×C19 ⋊ C3×C4
HallC11×Dic19 ⋊ ΓL(1,𝔽8)
HallC7×Dic19 ⋊ C3×C11
Hall#87704 ⋊ C4×C11
HallC11×C19 ⋊ C4×ΓL(1,𝔽8)
HallC7×C11 ⋊ (C19⋊C3)⋊C4
HallDic19 ⋊ C11×ΓL(1,𝔽8)
SylowC19 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C11×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C11#11716321
commutator, hypocenterC7×C19C3×C4×C11
FrattiniC2C11×#11716321
Fitting, socleC2×C7×C11×C19C2×C3
prime radicalC2×C11×#87704C2
cosocleC2×C7×C19C2×C3×C11
LCSG ▷ C7×C19
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5852

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 23);