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C3×C52×Dic77 #37528405

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C52×Dic77

Splittings

derived, HallC7×C11 ⋊ C3×C4×C52
HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ C3×Dic7
HallC3×C7×C11 ⋊ C4×C52
HallC52×C7 ⋊ C3×Dic11
HallC3×C11 ⋊ C52×Dic7
HallC3×C7 ⋊ C52×Dic11
SylowC11 ⋊ C3×C52×Dic7
SylowC7 ⋊ C3×C52×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D77
commutator, hypocenterC7×C11C3×C4×C52
FrattiniC2C3×C52×D77
Fitting, socle, prime radicalC2×C3×C52×C7×C11C2
cosocleC2×C7×C11C2×C3×C52
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C52

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 216);