Finite Group Databasebeta

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C112×#1039⋊C3 #49137293

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C5×C11

Aliases

direct productC112×#1039⋊C3
unambiguous semidirect product#1039⋊(C3×C112)
unambiguous semidirect product(C11×#1039)⋊(C3×C11)

Splittings

derived, SylowC52 ⋊ C3×C4×C112
HallC112×#1039 ⋊ C3
HallC112×C52⋊C3 ⋊ C4
HallC52×C112 ⋊ C3×C4
Hall#1039 ⋊ C3×C112
HallC52⋊C3 ⋊ C4×C112

Subgroups

subgroupG/H
center, hypercenterC2×C112(C5⋊D5)⋊C3
commutator, hypocenterC52C3×C4×C112
FrattiniC2C112×(C5⋊D5)⋊C3
Fitting, socleC2×C52×C112C2×C3
prime radicalC2×C112×C52⋊C3C2
cosocleC2×C52C2×C3×C112
LCSG ▷ C52
UCSC1 ◁ C2×C112

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7260

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 429);