Finite Group Databasebeta

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#555×C277 #31799689

order17728
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C277 · Schur multiplier (H2) = C23×C4

Aliases

direct product#555×C277

Subgroups

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

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8864

Conjugacy classes & character table

6925 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#47982250, #47982312, #47982395, …
maximal subgroup of#1624×C277, #1634×C277, #1646×C277, …
maximal normal subgroup of#1624×C277, #1634×C277, #1646×C277, …
maximal quotient of#2346×C277, #2354×C277, #2363×C277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17728, 236);