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C52×(C11⋊Dic11)⋊C3 #49137282

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5×C11

Aliases

direct productC52×(C11⋊Dic11)⋊C3

Splittings

derived, SylowC112 ⋊ C3×C4×C52
HallC52×C11⋊Dic11 ⋊ C3
HallC52×C112⋊C3 ⋊ C4
HallC52×C112 ⋊ C3×C4
HallC11⋊Dic11 ⋊ C3×C52
HallC112⋊C3 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52(C11⋊D11)⋊C3
commutator, hypocenterC112C3×C4×C52
FrattiniC2C52×(C11⋊D11)⋊C3
Fitting, socleC2×C52×C112C2×C3
prime radicalC2×C52×C112⋊C3C2
cosocleC2×C112C2×C3×C52
LCSG ▷ C112
UCSC1 ◁ C2×C52

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3300

Conjugacy classes & character table

1300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 418);