Finite Group Databasebeta

← Prev (#37528609) Next (#37528611) →

C3×C7×C11×#1042 #37528610

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C11×#1042

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derived, SylowC52 ⋊ C3×C4×C7×C11
HallC52×C7×C11 ⋊ C3×C4
HallC3×C52×C11 ⋊ C4×C7
HallC3×C52×C7 ⋊ C4×C11
HallC52×C11 ⋊ C3×C4×C7
HallC52×C7 ⋊ C3×C4×C11
HallC3×C52 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11#1042
commutator, hypocenterC52C3×C4×C7×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C5×C7×D5×C11C2
cosocleC5×D5C2×C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C3×C7×C11

104 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 56 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) = 4620

Conjugacy classes & character table

3003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 421);