Finite Group Databasebeta

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C3×C11⋊C5×Dic55 #49137249

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×Dic55

Splittings

derivedC5×C112 ⋊ C3×C4×C5
HallC3×C5×C11×C11⋊C5 ⋊ C4
HallC5×C11×C11⋊C5 ⋊ C3×C4
HallC3×C112 ⋊ C5×Dic5
SylowC112 ⋊ C3×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×D55
commutator, hypocenterC5×C112C3×C4×C5
FrattiniC2C3×C11⋊C5×D55
Fitting, socleC2×C3×C5×C112C2×C5
prime radicalC2×C3×C5×C11×C11⋊C5C2
cosocleC2×C5×C112C2×C3×C5
LCSG ▷ C5×C112
UCSC1 ◁ C2×C3

136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 3300

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 385);