Finite Group Databasebeta

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#562×C277 #31799696

order17728
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C277 · Schur multiplier (H2) = C24

Aliases

direct product#562×C277

Subgroups

subgroupG/H
center, socleC22×C277C24
commutator, Frattini, cosocleC22C24×C277
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C277 ◁ G

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8864

Conjugacy classes & character table

5263 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#47982460, #47982484, #47982490
maximal subgroup of#1656×C277, #1661×C277, #1662×C277, …
maximal normal subgroup of#1656×C277, #1661×C277, #1662×C277, …
maximal quotient of#2376×C277, #2377×C277, #2378×C277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17728, 243);